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Entanglement evolution of three-qubit mixed states in multipartite cavity - Reservoir systems

Jingzhou Xu, Jinbao Guo, Wen, Wei, Yan-Kui Bai, Fengli Yan

Published Jan 1, 2012• 7 citations
OpenAlex

Abstract

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.

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We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we also address the relationship between the genuine block-block entanglement form and qubit-block form in the interval.
We consider the entanglement dynamics of three two-level atoms interacting with independent structured non-Markovian reservoirs. The atoms are initially prepared in a mixed multipartite Greenberger—Horne—Zeilinger (GHZ)-type state. Based on the purity and non-Markovian reservoirs, we show that the reservoirs' entanglement can exhibit not only multipartite entanglement sudden birth but also entanglement sudden death, and the revival of atom entanglement is not always accompanied by the disentanglement of reservoirs. Meanwhile, we derive the quantitative criteria for multipartite revival and death phenomena and find multipartite entanglement sudden death and entanglement sudden birth simultaneous apparition time is independent of the initial three-qubit state.
The maximally entangled state can be the mixed state form beside the well-known pure state case. As quantified by the negativity, we study the entanglement dynamics of bipartite mixed maximally entangled state (MMES) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different to the asymptotic decay of pure state case. Moreover, we find that the maximal entanglement cannot guarantee the maximal nonlocality. The measurement-induced nonlocality (MIN) of MMES is not always the maximal, and its value and dynamical behavior are dependent on the mixed probability. In addition, we investigate the distributions of negativity and MIN in the multipartite system, where the two types of correlations have different monogamous properties in the dynamical procedure.
In this paper, we consider the entanglement dynamics of two cavities interacting with independent reservoirs. When the cavity entanglement suddenly disappeared, the reservoir entanglement suddenly and necessarily appears. We study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. Also, we find that the conditions on the apparition of the entanglement sudden death and the entanglement sudden birth can be generalized when the initial entangled state of cavities is not pure, which is a complement to the result in the paper [Phys. Rev. Lett.101 (2008) 080503] for the pure case.
We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find also that when the cavity entanglement suddenly disappears, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this entanglement sudden birth can manifest before, simultaneously, or even after entanglement sudden death. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.